Joe Cocker did a pretty sweet rendition of 'With A Little Help From My Friends'. I prefer it over the original version. Don't know about the other acts and songs performed. Maybe, Jimi Hendrix covered something.

Richie Havens did With a Little Help From My Friends, Strawberry Fields Forever, and Hey Jude. Joe Cocker did With a Little Help From My Friends. CS&N did Blackbird. I know RH did a pretty famous cover of Here Comes the Sun, evidently not at Woodstock.

And Jimi Hendrix' song was Hey Joe not Hey Jude - a totally different composition. Jimi did cover Beatles but not at Woodstock. Can't add anything to Col A's answer since I wasn't there personally and it's what the official setlist says too.

(Don't you dare answer this Col. and get yourself disqualified! )

__________________

Sometimes I dream in colors
It always happens when
I find myself with others
Who don't pretend

Richie Havens did With a Little Help From My Friends, Strawberry Fields Forever, and Hey Jude. Joe Cocker did With a Little Help From My Friends. CS&N did Blackbird. I know RH did a pretty famous cover of Here Comes the Sun, evidently not at Woodstock.

You got it.

Richie Havens didn't do Here Comes The Sun, but he did do the other three songs you mention.
And he didn't know all the words because he was improvising a lot (though his Strawberry Fields is exceptional).
Even his famous song Freedom in the film was an improvisation.